Bayern entered the second leg of the last-16 tie boasting a 5-0 advantage from their clash at the Allianz Arena last month.
The German champions followed up that result with a 3-1 success in Turkey as they cruised into the final eight of the competition once again.
Bayern should have led inside the first 10 minutes of the second leg when Thomas Muller reacted first to a loose Tolga Zengin save inside the Besiktas box, but the German attacker fired over the crossbar.
The visitors did lead eight minutes later, however, when Muller's excellent cross found Thiago, with the midfielder placing the ball into the back of the net from close range.
Besiktas's best chance of the first period fell to Ricardo Quaresma in the 38th minute, but the Portuguese saw his free kick just miss the crossbar.
Bayern were a threat every time they had the ball, however, and their second arrived shortly after the interval when Gokhan Gonul turned into the back of his own net from close range.
Besiktas did have one back just before the hour when Vagner Love slotted into the bottom corner of the net.
The hosts missed a wonderful chance to level in the 62nd minute though when Mustafa Pektemek somehow headed a Quaresma cross over the Bayern goal from close range.
James Rodriguez passed up a good opportunity to score Bayern's third in the 76th minute when he missed the post with a powerful strike, but the visitors did take a 3-1 lead in the 84th minute when Sandro Wagner converted from close range.
BESIKTAS (4-4-2): Zengin; Erkin, Uysal, Medel, Gonul; Lens (Talisca 60'), Arslan (Hutchinson 60'), Oyzakup, Quaresma; Pektemek, Love (Babel 75')
BAYERN (4-3-3): Ulreich: Rafinha, Boateng, Hummels (Sule 46'), Alaba; Vidal, Martinez, Thiago (James 35'); Muller, Lewandowski (Wagner 68'), Riberty